LIQUIDUS SURFACE AND SPINODAL OF Fe-B-C ALLOYS

In this work the study is performed for the specimens of Fe-B-C alloys with boron content of 0.005–7.0 wt. % and carbon content of 0.4–6.67 wt. %, the rest is iron. According to the findings of microstructure analysis, XRD and differential thermal analyses, the primary phases and the temperatures of their formation are determined. Depending on boron content (in the range of 1.5–8.80 wt. %) and carbon content (0.5–6.67 wt. %) in the Fe-B-C alloys, the primary phases in the process of crystallization are γ -Fe, boron cementite Fe 3 (CB) and boride Fe 2 В . The outcomes of the experiment carried out in this work determine the phase composition and phase transformations occurring in the alloys and the liquidus surface is constructed. The findings show that the liquidus temperature for Fe-B-C system alloys is low compared to binary Fe-B and Fe-C alloys. At the liquidus surface of the Fe-B-C alloys, there is a point at boron content of 2.9 wt. % and carbon content of 1.3 wt. % with the lowest temperature of 1375 K and it is the point of intersection of monovariant eutectics. This fact is in a good agreement with the results of other authors. The microstructure of alloys located at the curves of monovariant eutectics is represented by the γ –Fe+Fe 2 B and γ –Fe+Fe 3 (CB) eutectics and the primary crystals of Fe 2 B iron boride in the shell of Fe 3 (BC) boron cementite. In this paper it is shown experimentally the existence of a quasi-binary section and the coordinates of the peritectic point are fixed: the boron content is 5.0 wt. %, carbon content is 3.0 wt. % and the temperature is 1515 K. The free energy of the Fe-B-C melt is calculated for the first time by the quasi-chemical method and the surface of thermodynamic stability of the Fe-B-C melt is plotted, depending on temperature and boron and carbon content in the alloy. The results obtained in the paper show that in order to obtain a homogeneous Fe-B-C melt, which does not contain any microheterogeneous structure in the form of short-order microregions, it is necessary to perform the overheating more than to 180 K for the region where the primary phase is iron, and no less than to 200 K for the regions with boron cementite and boride.


EEJP. 1 (2020)
Natalia Yu. Filonenko, Alexandra N. Galdina atmosphere. The cooling rate of the alloys was 20 K/min. To determine the chemical composition of alloys, chemical and spectral analyses were used [11]. To reveal the peculiarities of phase transformations in the Fe-B-C system alloys, differential thermal analysis (DTA) of 72 specimens was performed by means of derivatograph. The phase composition of alloys was studied by method of X-ray microanalysis by means of JSM-6490 microscope with ASID-4D scanning head and "Link Systems 860" software energy-dispersive X-ray microanalyser, and by means of optical microscope "Neophot-21". The X-ray electron probe analysis was carried out using internal standards. The X-ray and X-ray diffraction analyses were performed with DRON-3 diffractometer in monochromated Fe-Кα radiation.

RESULTS AND DISCUSSION
Study of the liquidus temperature in the Fe-B-C system alloys and the primary phases in relation to boron and carbon content, shows that at 3.0 wt. % boron and 0.65 wt. % carbon the formation of γ-Fe primary crystals occurs while crystallization in the temperature range of 1417-1420 K. In the temperature range of 1397-1403 K the γ-Fe+Fe 2 B eutectics formation occurs, and at 1393-1396 K the γ-Fe+Fe 3 (CB) eutectics appears. The γ-Fe↔α-Fe transformation takes place at the temperature of 996 K (Fig. 1). Investigation of the alloys with 0.3-5.5 wt. % boron and 2.1-6.6 wt. % carbon shows that the primary crystals in the process of crystallization are Fe 3 (CB) boron cementite formed within the temperature range of 1427-1431K. At further cooling the formation of the γ-Fe+Fe 3 (CB) eutectics with lamellar morphology is observes in the temperature range of 1387-1403 K (Fig. 2). The γ-Fe↔α-Fe transformation is detected at the temperature of 973 K.
The results of durometric analysis reveals that the microhardness of boron cementite is 723.1 GPa, and that for the γ-Fe+Fe 3 (CB) eutectics is 675.8 GPa. For the alloys with 2.2-8.8 wt. % boron and 0.5-2.1 wt. % carbon during the crystallization the formation of primary crystals of Fe 2 B iron boride occurs. In certain parts of the structure the primary borides are observed surrounded with the shell consisting of Fe 3 (BC) boron cementite and the α-Fe+Fe 3 (BC) eutectics with morphology similar to that of the boride eutectics (α-Fe+Fe 2 B) (Fig. 3a).
The results of differential thermal analysis indicates that the primary crystals of boride are formed from the melt in the temperature range of 1498-1533 K and surrounded with boron cementite shell appeared during the peritectic transformation 2 3 L + Fe B Fe (CB)  at 1388-1433 K; the γ-Fe+Fe 3 (CB) eutectics is formed at the constant temperature of 1399 K, which implies the possibility of the four-phase transformation The findings show that the liquidus temperature for Fe-B-C system alloys is low compared to binary Fe-B and Fe-C alloys. This is in agreement with the results of other authors [12].
The study of microstructure, XRD and DTA for 72 specimens allows us to construct the liquidus surface for the alloys of Fe-B-C system (Fig. 4).
One of the important factors affecting the formation of the alloys structure under cooling is determination of the liquid stability, i.e. the temperature when the homogeneity of the liquid is observed and there are no any microcrystalline formations.
The Helmholtz free energy is known to be a function of independent variables i ( , , ) . Provided that there are no any external force and change in volume ( const V  , const p  ) the total differential of Helmholtz free energy is written in a form , where U is the internal energy. Correspondingly, the thermodynamic forces are the entropy , and the chemical potential of the constituent in compound To determine the phase stability, let us find the variation of Helmholtz free energy: (1) The general condition of the phase stability by Gibbs is that arbitrary variations of the internal energy and external parameters of the system should not cause both reversible and irreversible processes in the system (to keep the system in equilibrium), so they must be such that [13]: So, to determine the thermodynamic stability of the Fe-B-C system melt, we use the approach proposed by the author of [14].
The determinant of stability for the melt is:  x The case of D=0 was first defined by J. W. Gibbs as a critical state of matter [15]. During the supercritical transitions the determinant and coefficients of stability pass through finite minima that correspond to the growth of fluctuations. The locus of these minima is a low-stability curve. It should be noted that for different coefficients of stability, the curves of lowered stability may not be coinciding. For these reasons the curve of lowered stability for D, which includes all equilibrium characteristics of the system and therefore best describes its stability, is used as a basis. The threshold case of supercritical transitions when fluctuations in the system reach the maximum level, the determinant and coefficients of stability pass zero minima, is the critical state. So, let us find when dD=0.
The Helmholtz free energy we find by the quasi-chemical method as: where T is the temperature (K), ij  is the interaction energy of components (J/mol).
To calculate the free energy of the melt, we used the values of energies of interactions between the components from the works [15][16][17][18][19][20]. The sum is taken over all і and j provided j i  .
From Eq. (4) we obtain the thermodynamic functions of the melt:

CONCLUSION
In the paper the phase composition and phase transformation occurring in the alloys with boron content of 0.005-7.0 wt. % and carbon content of 0.4-6.67 wt. % (the rest is iron) is studied. It is shown that formation of the primary phases γ-Fe, Fe 2 B and Fe 3 (CB) takes place depending on boron and carbon content in the alloys.
The liquidus surface is plotted experimentally for the Fe-B-C system alloys in the concentrarion range of 0-8.85 wt. % boron and 0-6.65 wt. % carbon and it is shown that the ternary eutectic point occurs at the liquidus surface in the alloys of Fe-B-C systems with boron content of 2.9 wt. % and carbon content of 1.3 wt. % at the temperature of 1375 K.
In this paper, using the quasi-chemical methos, we obtain for the first time the temperature dependence of the Helmholtz free energy of the Fe-B-C melt. We obtain the dependences of the temperature of thermodynamic stability of the melt on boron and carbon content in the alloy and plot the surface of concentration anomaly without any microcomplexes in the melt. According to the outcomes, it is necessary to perform the overheating more than to 180 K to obtain the homogeneous Fe-B-C melt, which does not contain the microheterogeneous structure in the form of shortorder microregions.